We propose a novel Stark decelerator for atoms or molecules excited in Rydberg states, in which the electric field continuously follows the motion of particles. Using moderate m Rydberg states (m > 2) in low-field seeker Stark levels, the evolution in the decelerator field should be hydrogen-like. Furthermore, the electric field seen by the particles is roughly constant; this greatly reduces the losses due to electric field induced transitions. We show that this decelerator fulfils the requirement of phase-space stability, since it is equivalent to a smoothly travelling well. This kind of decelerator should provide a new tool to obtain cold molecules, and is applicable to a very large range of molecules. Numerical simulation shows that within times compatible with Rydberg lifetimes, a cloud of sodium atoms can be stopped in the laboratory frame from a supersonic beam.